Basic partial fractions decomposition

2 Express \(\frac { x + 1 } { ( 2 x - 1 ) }\) in partial fractions.

2 Express \(\frac { 13 - x } { ( x - 3 ) ( x + 2 ) }\) in partial fractions.

2 Express \(\frac { 5 x + 1 } { x ^ { 2 } - x - 12 }\) in partial fractions.

3. Express \(\frac { 9 x ^ { 2 } + 43 x + 8 } { ( 3 + x ) ( 1 - x ) ( 2 x + 1 ) }\) in partial fractions.
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[0pt] [BLANK PAGE] The matrix \(\mathbf { A }\) is given by \(\mathbf { A } = \left( \begin{array} { l l } 2 & a
0 & 1 \end{array} \right)\), where \(a\) is a constant.

1. Find \(\mathrm { A } ^ { - 1 }\). The matrix \(\mathbf { B }\) is given by \(\mathbf { B } = \left( \begin{array} { l l } 2 & a
   4 & 1 \end{array} \right)\).
2. Given that \(\mathrm { PA } = \mathrm { B }\), find the matrix P .
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5 Express $$\frac { 5 ( x - 3 ) } { ( 2 x - 11 ) ( 4 - 3 x ) }$$ in the form $$\frac { A } { ( 2 x - 11 ) } + \frac { B } { ( 4 - 3 x ) }$$ where \(A\) and \(B\) are integers.